Transition Algebra is the first theoretical course in Classic Math School’s Enrichment Program, and intended for students from 5th to 8th grade. This course prerequisites include well-developed number sense: the fluency with all arithmetic operations on whole numbers, fractions and decimals, plus a certain level of mathematical maturity.  The scope and depth of the course may vary significantly depending on the actual students’ level and duration of the course.

 

The key elements of Transition Algebra Course:

  1. Number Theory.
  2. Linear equations and inequalities in one variable.
  3. Modeling word problems with algebraic expressions, equations and inequalities.

Concepts introduction and problem solving form an integral part of each class session. Students learn extensively from and by examples, and through problem discussions. A variety of instructional methods are used to enhance students' problem-solving abilities. Students tackle many complicated problems using inductive and deductive reasoning approaches.

 

The topics and problems that are studied in Transition Algebra course may include:

 

Introduction to Number Theory. Rules of Divisibility and their Proofs.

Prime and Composite Numbers. Sieve of  Eratosthenes. Relatively Prime Numbers.

Prime Factorization. Different Algorithms to find GCF and LCM.

Fundamental Theorem of Arithmetic.

Integral Exponents. Quadratic and Cubic Radicals.

 

Introduction to the Structure of Real Number Set and its Subsets.

Natural Numbers. Whole Numbers. Integers. Rational Numbers. Irrational Numbers (proof of existence).

Converting Fractions to Decimals and Decimals to Fractions.

Terminating , Non-terminating , Repeating and Nonrepeating Decimals.

Different Strategies of Converting Fractions to Decimals and Decimals to Fractions.

 

Comparing and Ordering Real Numbers. Number Line. Trichotomy Property of Real Numbers. Density of Rational/Real Numbers.

Operations with Real Numbers.  Order of Operations as a Convention.

Properties of Operations with Real Numbers:

Commutative, Associative, Identity, Distributive, Closure.

Additive Inverses. Reciprocals.

 

Variables. Algebraic Expressions. Evaluation and Transformation of Algebraic Expressions.

Equivalent Algebraic Expressions.  Identities Versus  Equations.

Factoring. Collecting Like Terms. Simplifying Algebraic Expressions.

Translation between Words and Algebraic Expressions.

 

Equations. General Algorithm for Solving Linear Equations with One Variable.

Equations Having Infinite Number of Solutions. Equations Having no Solutions.

Translation between Sentences and Equations.

 

Inequalities. General Algorithm for Solving Linear Inequalities with One Variable.

Graphing Inequalities. Set Notation for Solutions of Inequalities.

Translation between Sentences and Inequalities.

Word Problems Leading to Linear Inequalities with One Variable.

 

Ratios and Rates. Proportions. Extremes and Means of a Proportion. Cross Products.

Solving Proportions. God Proportion. Similar Figures.

Percents. Three Basic Types of Percent Equations.  Percent Word Problems.

Inverse proportions. Word problems Leading to Direct and Inverse Proportions.

 

General Strategy for Solving Word Problems Leading to Equations.

Word Problems Leading to Linear Equations with One Variable.

Area – Perimeter Problems. Coin Problems. Motion Problems. Age Problems.

Investment Problems.  Mixture Problems. Work (Productivity) Problems.